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Simplifying n2 + -12n + -7 = 0 Reorder the terms: -7 + -12n + n2 = 0 Solving -7 + -12n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -12n + 7 + n2 = 0 + 7 Reorder the terms: -7 + 7 + -12n + n2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -12n + n2 = 0 + 7 -12n + n2 = 0 + 7 Combine like terms: 0 + 7 = 7 -12n + n2 = 7 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = 7 + 36 Reorder the terms: 36 + -12n + n2 = 7 + 36 Combine like terms: 7 + 36 = 43 36 + -12n + n2 = 43 Factor a perfect square on the left side: (n + -6)(n + -6) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (n + -6) equal to 6.557438524 and -6.557438524.Subproblem 1
n + -6 = 6.557438524 Simplifying n + -6 = 6.557438524 Reorder the terms: -6 + n = 6.557438524 Solving -6 + n = 6.557438524 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 6.557438524 + 6 Combine like terms: -6 + 6 = 0 0 + n = 6.557438524 + 6 n = 6.557438524 + 6 Combine like terms: 6.557438524 + 6 = 12.557438524 n = 12.557438524 Simplifying n = 12.557438524Subproblem 2
n + -6 = -6.557438524 Simplifying n + -6 = -6.557438524 Reorder the terms: -6 + n = -6.557438524 Solving -6 + n = -6.557438524 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -6.557438524 + 6 Combine like terms: -6 + 6 = 0 0 + n = -6.557438524 + 6 n = -6.557438524 + 6 Combine like terms: -6.557438524 + 6 = -0.557438524 n = -0.557438524 Simplifying n = -0.557438524Solution
The solution to the problem is based on the solutions from the subproblems. n = {12.557438524, -0.557438524}
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